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Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on C0
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  • Published: 03 May 2005

Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on C0

  • Sönke Blunck1 

Probability Theory and Related Fields volume 133, pages 71–97 (2005)Cite this article

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Abstract

Given γ ∈ (−1,1), we present a dyadic growth condition on the finite dimensional distributions of operator semigroups on C0(E which - for γ>0 and Feller semigroups - assures that the corresponding Feller process has paths in local Hölder spaces and in weighted Besov spaces of order γ. We show that, for operator semigroups satisfying Gaussian kernel estimates of order m>1, condition holds for all and even for all in the case of Feller semigroups. Such Gaussian kernel estimates are typical for Feller semigroups on fractals of walk dimension m and for semigroups generated by elliptic operators on ℝD of order m≥D.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Cergy-Pontoise, 2, avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France

    Sönke Blunck

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  1. Sönke Blunck
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Correspondence to Sönke Blunck.

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Blunck, S. Path regularity for Feller semigroups via Gaussian kernel estimates and generalizations to arbitrary semigroups on C0. Probab. Theory Relat. Fields 133, 71–97 (2005). https://doi.org/10.1007/s00440-004-0415-2

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  • Received: 30 March 2004

  • Revised: 17 November 2004

  • Published: 03 May 2005

  • Issue Date: September 2005

  • DOI: https://doi.org/10.1007/s00440-004-0415-2

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Keywords

  • Assure
  • Growth Condition
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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